Dear Prof. Van Buren, like any other videos that you created, this is also a master piece. I follow and learn a lot with your explanations, but I am not able to find how solve a problem. As a sailor, I learned that the max. speed that a displacement boat can achieve is approximately 1.3 X length^1/2 (speed in knots, length in feet). How can I deduct this? The wave that is generated at the front of the boat have a length equal the length of the boat why? If you cant help me to find some source of info about this problem I really appreciate. Again, congratulations for the fantastic Elio Somaschini
Thanks again for the kind words! Long comment below: I'm no boat or surface wave expert at all, but here's my interpretation after a bit of background searching and asking friends who know a bit more about boat stuff. First, when a boat moves through water it needs to push water out of the way, this creates a wave at the bow. This wave has a speed "c", and the speed of this wave goes as "c = sqrt(g L_w/2 pi)" where "g" is gravitational acceleration and "L_w" is the wavelength (this wave speed stuff was originally found by Lord Kelvin!). Some of the square-rooted terms are constants, so this is roughly "c = 1.3 * sqrt(L_w)" where the unit of speed here are knots. So we need to now understand what controls the bow wave length, "L_w". The wave velocity "c" is a direct function of the boat velocity "v". The next time you're standing on your boat moving at a constant velocity, if you look at the wake you will notice the wake is frozen or steady relative to the boat. This is because the boat creates waves with a velocity close to the boat. So, if the boat speed "v=c", then the boat speed directly controls the wave length of the bow wave, "L_w". As boat velocity goes up, so does the bow wave length. At low boat velocities, there are multiple waves that fit under the hull, so the boat rests nicely on all these peaks/troughs and stays relatively flat. But, at some point as the boat velocity increases, it creates a wave with the same length as the boat. So, the boat only fits on a single bow wave, and it starts to angle upwards as if climbing it like a hill (it's like the opposite of a surfer, who rides down the "hill" of a wave). You can imagine that as you try and climb the "hill" of the single big wave you are making, you spend a lot of energy because now your propulsion needs to counter gravity. This dramatically increases the effective drag and presents the limit in velocity. This means we do not want to make waves that equal the boat length, so we don't want "L_b = L_w". Going back to our original equation for wave speed, "c = v = sqrt(g L_w/2 pi) = 1.3 sqrt(L_w)". So, you want to stay below the boat velocity "v" that gives you "L_w=L_b", giving you a limit on your boat velocity "v
It depends on the flow, but yes in the statistical point-of-view it can still hold true. Instantaneously, velocity can be maximum off center in something like turbulent pipe flow, but in the time-average it is still max at the center. We use RANS to consider the equations in the time-average sense.
![Turbulence [Fluid Mechanics #10]](/img/logo.svg){kind=logo}
